Madison is an extremely liveable city. It's not big, but it's also not the country. There are plenty of restaurants (lots of different ethnic foods), lots of lakes and trails and outdoor activities. For a city its size, it even has a decent amount of museums, theatres, music venues, etc.The winters are brutal, but the summers are hot and fall is absolutely beautiful. Most people really like it. There's a discussion thread here:
San Diego would for sure win in the weather category though. Cost of living is something else to factor in. San Diego is one of the most expensive places to live in the country, whereas Madison is pretty cheap. Even if the stipend at UCSD will be higher in subsequent years, it may not go as far as the same or a smaller amount would in Wisconsin.
Good luck with your decision!